Which set of numbers is the largest family group that includes all the others rational numbers natural numbers real numbers irrational numbers
The set of real numbers is the largest family group that includes all the other sets mentioned (rational numbers, natural numbers, and irrational numbers).
The set of real numbers is the largest family group that includes all the other sets mentioned.
Here is the hierarchy of the sets you mentioned, from smallest to largest:
1. Natural numbers: These are the numbers 1, 2, 3, 4, and so on. Natural numbers are a subset of the set of rational numbers.
2. Rational numbers: These are numbers that can be expressed as a fraction, where the numerator and denominator are both integers. Rational numbers include natural numbers and integers, as well as numbers such as 1/2, 7/5, -3/4, and so on.
3. Irrational numbers: These are numbers that cannot be expressed as a fraction and do not terminate or repeat indefinitely. Examples of irrational numbers include square roots of non-perfect squares (such as √2, √3), transcendental numbers (such as π and e), and certain decimal representations (such as 0.101001000100001...).
4. Real numbers: This is the largest set that includes all the numbers mentioned above. The set of real numbers includes both rational and irrational numbers. Real numbers also include numbers such as whole numbers, integers, and fractions, as well as numbers that cannot be represented as fractions or decimals.
So, the real numbers encompass all rational numbers (including natural numbers) and irrational numbers, making it the largest family group.